Low-Rank Matrix Estimation in the Presence of Change-Points

被引：0
|
作者：
Shi, Lei [1 ]
Wang, Guanghui [2 ,3 ]
Zou, Changliang [3 ,4 ]
机构：
[1] Univ Calif Berkeley, Dept Biostat, Berkeley, CA 94704 USA
[2] Nankai Univ, Sch Stat & Data Sci, LPMC, KLMDASR, Tianjin 300071, Peoples R China
[3] Nankai Univ, LEBPS, Tianjin 300071, Peoples R China
[4] Nankai Univ, Sch Stat & Data Sci, NITFID, LPMC,KLMDASR, Tianjin 300071, Peoples R China
来源：
JOURNAL OF MACHINE LEARNING RESEARCH | 2024年 / 25卷
基金：
国家重点研发计划; 上海市自然科学基金; 中国国家自然科学基金;
关键词：
High-dimensional data; low-rank estimation; multiple change-point detection; non-asymptotic bounds; rate-optimal estimators; COMPLETION; REGRESSION; RECOVERY; NUMBER;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider a general trace regression model with multiple structural changes and propose a universal approach for simultaneous exact or near-low-rank matrix recovery and changepoint detection. It incorporates nuclear norm penalized least-squares minimization into a grid search scheme that determines the potential structural break. Under a set of general conditions, we establish the non-asymptotic error bounds with a nearly-oracle rate for the matrix estimators as well as the super-consistency rate for the change-point localization. We use concrete random design instances to justify the appropriateness of the proposed conditions. Numerical results demonstrate the validity and effectiveness of the proposed scheme.
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页数：71
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